The article is not written from a polemical angle, but rather is motivated by an endeavour to extend critical rationalism beyond the bounds of Albert’s version of the doctrine. In this I am guided by these main theses: I. Albert does not distinguish the rejection of the argument of final justification from the argument of sufficient, not only final, justification, valid in the case of trivial knowledge in our “middle world”. II. If critical rationalism is going to cover not just a segment, but the whole of reality, as Albert would like, then necessarily it must give attention to existential elements when we are confronted with extreme situations in which argument takes the form of our very existential decision. III. I do not think that Albert should abandon his atheism and I, too, am a convinced atheist. However, if his critical attitude to the phenomenon of Christian faith is to be suffiently rational, he cannot overlook the anthropological dimensions of Christian faith and their heights. IV. Critical rationalism has not, in my opinion, addressed two basic questions: 1) Is capitalism a humanism? 2) Should the question of private property be the object of critical re-examination – especially with regard to the conditional problems of the globalising world. V. Even allowing for the fact that Albert, in his last writings, toned down his former disdain for psychology, we should recognise that addressing problems and contexts in which discoveries are made always has a psychological accompaniment.